In the original video, we used 1/4" rope, but have moved to 1/2 inch cotton rope, as it did a better job spreading the braids apart than the 1/4 rope did.
5/8 rope is what we normally use in our B24 power cables, so it's possible you did get the larger 5/8 rope by accident, which is a bit of a tight fit for the 16-strand cable. I definitely had a similar issues feeding 5/8" polyethylene rope through my 16-strand cables as well.
It won't hurt performance tho, just takes a little more effort to feed through.